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1.
We analyze the general 2D isosceles three-body problem for various ratios ? of the mass of the central body to the mass of each of the other two bodies. We set the initial conditions using two parameters: the virial coefficient k and the parameter \(\mu = \dot r/\sqrt {\dot r^2 + \dot R^2 }\), where \(\dot r\) is the relative velocity of the two outer bodies and \(\dot R\) is the velocity of the central body relative to the center of mass of the outer bodies. We compare statistical dependences between evolutionary parameters of triple systems with various values of ?, and analyze the k and μ dependences of the number of crossings of the center of mass of the triple system by the central body and the lifetime of the system. We construct the functions Rmax(rmax), where rmax and Rmax are the maximum achievable distances between the outer bodies, and between the central body and the center of mass of the outer bodies in the triple system. The parameter ? proves to be the most important parameter of the problem, and determines the relationship between the measures of the regular and stochastic trajectories. However, there exist “seeds” of stochasticity, even at small ?～10?2. The measure of the stochastic orbits increases with ?; when ?≥10, virtually the entire region of the initial conditions corresponds to stochastic trajectories.  相似文献   

2.
The paper considers triple encounters in the linear three-body problem for the case of equal masses. Triple encounters are described using two parameters: the virial coefficient k and the angle ? such that tan $\varphi = \dot r/\dot \rho$ , where $\dot r$ and $\dot \rho$ are the velocities of the “central” body relative to each of the “outer” bodies. The equations of motion are integrated numerically up to one of the following times: the time for a receding body to turn, the time for this body to reach some critical distance, the time for some escape criterion to be fulfilled, or to some critical time. Evolutionary scenarios for the triple system are determined as a function of the initial conditions. The dependences of the ejection length on k and $\dot \varphi$ are derived. The initial conditions corresponding to escape form a continuous region with k>0.5. The regions into which the right and left bodies depart alternate and are symmetrical about the lines of triple close encounters (?=45°,225°). Regions of stable motions in the vicinity of the central periodic orbit of Schubart (k?0.206; ?=135°,315°) are identified. Linear structures emanate from the peak of the region of stability, which divide the region for the initial conditions into alternating zones with identical evolutionary scenarios.  相似文献   

3.
We have modeled the dynamical evolution of small stellar groups with N=6 components in the framework of the gravitational N-body problem, taking into account possible mergers of stars and ejection of single and binary stars. We study the influence of the initial global parameters of the systems (the mass spectrum, average size, virial factor) on their dynamical evolution. The distribution over states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of binary and stable triple systems that form are studied, as well as the properties of ejected single and binary stars. The rate of dynamical evolution in both expanding and contracting groups is higher than in systems in a state of virial equilibrium. The dynamical evolution is more intense in the case of unequal masses than when the system initially consists of equal-mass stars. In most cases, the evolution of a group ends with the formation of a binary or stable triple system. The semimajor axes of the binaries range from several hundredths to several times the initial size of the system. The distribution of the eccentricities of the binaries formed is consistent with an f(e)=2e law. When the initial size of the group is small, the number of final binaries with large eccentricities, and also of stable triple systems with elongated inner-binary orbits, decreases due to merging. As a rule, stable triple systems are substantially hierarchical (the average ratio of the semimajor axes of the inner and outer binaries is 1: 20). On average, the eccentricities of the inner binaries exceed those of the outer binaries: they are equal to \(\overline {e_{in} } \approx 0.7\) and \(\overline {e_{ex} } \approx 0.5\), respectively. The velocities of ejected stars are from several to several tens of km/s, and tend to increase as the initial size of the system, and hence its virial coefficient, decreases.  相似文献   

4.
Orbital-period variations of the eclipsing binaries FK Aql and FZ Del are analyzed. For each of the systems, a superposition of two cyclic variations of their orbital periods is found. FK Aql may be a quadruple system that contains two more bodies, besides the eclipsing binary, with masses M 3 ? 1.75M ⊙ and M 4 ? 1.47M ⊙, and the corresponding periods 15 and 82 yrs. This could also be a triple system with a third body of mass M 3 ? 1.75M ⊙ and a period of the long-period orbit P 3 = 15 yrs, or with a third body of mass M 3 ? 1.30M ⊙ and a period of the long-period orbit P 3 = 82 yrs. FZ Del may be a quadruple system with the additional componentmasses M 3 ? 0.2M ⊙ and M 4 ? 0.3M ⊙, with the periods 10.2 and 53.7 yrs. This could also be a triple system with a third-body mass M 3 ? 0.2M ⊙ and a period of the long-period orbit P 3 = 10.2 yrs. In both systems, the residual period variations could be due to magnetic cycles of the secondary. The period variations of the eclipsing binary FZ Del could also be due to apsidal motion, together with the influence of a third body or the effects of magnetic activity.  相似文献   

5.
N-body dynamical simulations are used to analyze the conditions for the gravitational stability of a three-dimensional stellar disk in the gravitational field of two rigid spherical components—a bulge and halo whose central concentrations and relative masses vary over wide ranges. The number of point masses N in the simulations varies from 40 to 500 000 and the evolution of the simulated systems is followed over 10–20 rotation periods of the outer edge of the disk. The initially unstable disks are heated and, as a rule, reach a quasi-stationary equilibrium with a steady-state radial-velocity dispersion cr over five to eight turns. The radial behavior of the Toomre stability parameter QT(r) for the final state of the disk is estimated. Simple models are used to analyze the dependence of the gravitational stability of the disk on the relative masses of the spherical components, disk thickness, degree of differential rotation, and initial state of the disk. Formal application of existing, analytical, local criteria for marginal stability of the disk can lead to errors in cr of more than a factor of 1.5. It is suggested that the approximate constancy of QT?1.2–1.5 for r?(1–2)×L (where L is the radial scale of disk surface density), valid for a wide range of models, can be used to estimate upper limits for the mass and density of a disk based on the observed distributions of the rotational velocity of the gaseous component and of the stellar velocity dispersion.  相似文献   

6.
The evolution of Population I stars with initial masses 60 M ⊙ ≤ M ZAMS ≤ 120 M ⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T eff ～ 105 K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T eff ≈ 105 K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M ⊙ to M = 6 M ⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 105 K.  相似文献   

7.
We have modeled the dynamical evolution of small groups of N=3–18 stars in the framework of the gravitational N-body problem, taking into account possible coalescences of stars and the ejection of single and binary stars from the system. The distribution of states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of the binaries and stable triple systems formed, as well as those of ejected single stars, are studied. In most cases, the evolution of the group results in the formation of a binary or stable triple system. The orbital eccentricities of the binaries formed are distributed according to the law f(e)=2e. As a rule, stable triple systems display pronounced hierarchy (the mean ratio of the semimajor axes of the outer and inner binaries is about 20:1). Stars are ejected with velocities from several km/s to several tens of km/s. The results of the modeling are compared with the parameters of observed wide binaries and triple systems.  相似文献   

8.
Estimates of the masses of supermassive black holes (M bh ) in the nuclei of disk galaxies with known rotation curves are compared with estimates of the rotational velocities V m and the “indicative” masses of the galaxies M i . Although there is a correlation between M bh and V m or M i , it is appreciably weaker than the correlation with the central velocity dispersion. The values of M bh for early-type galaxies (S0-Sab), which have more massive bulges, are, on average, higher than the values for late-type galaxies with the same rotational velocities. We conclude that the black-hole masses are determined primarily by the properties of the bulge and not the rotational velocity or the mass of the galaxy.  相似文献   

9.
A systematic analysis ofmethods for computing the trajectories of solid-phase particles applied in modern astrophysics codes designed for modeling gas–dust circumstellar disks has been carried out for the first time. Themotion of grains whose velocities are determinedmainly by the gas drag, that is, for which the stopping time or relaxation time for the velocity of the dust to the velocity of the gas tstop is less than or comparable to the rotation period, are considered. The methods are analyzed from the point of view of their suitability for computing the motions of small bodies, including dust grains less than 1 μm in size, which are strongly coupled to the gas. Two test problems are with analytical solutions. Fast first order accurate methods that make it possible to avoid additional restrictions on the time step size τ due to gas drag in computations of the motion of grains of any size are presented. For the conditions of a circumstellar disk, the error in the velocity computations obtained when using some stable methods becomes unacceptably large when the time step size is τ > tstop. For the radial migration of bodies that exhibit drifts along nearly Keplerian orbits, an asymptotic approximation, sometimes called the short friction time approximation or drift flux model, gives a relative error for the radial-velocity computations equals to St2, where St is the Stokes number, the ratio of the stopping time of the body to some fraction of the rotation period (dynamical time scale) in the disk.  相似文献   

10.
Variations of the orbital periods of the eclipsing binaries TU Cnc, VZ Leo, and OS Ori are analyzed. Secular period decreases were earlier believed to occur in these systems. It is demonstrated that the period variations of TU Cnc can be represented using the light-time effect corresponding to the orbital motion of the eclipsing binary with a period of 78.6 years around the center ofmass of the triple system, with the mass of the third body being M 3 > 0.82M ⊙. With the same accuracy, the period variations of VZ Leo and OS Ori can be represented either solely using the light-time effect, or a superposition of a secular period decrease and the light-time effect. For VZ Leo, the period of the long-term orbit is 63.8 years in the former case and 67.9 years in the latter case. Similar masses for the third body are indicated in both cases: M 3 > 0.55M ⊙ and M 3 > 0.61M ⊙. For OS Ori, the period of the long-term orbit is 46 years and M 3 > 0.5M ⊙ in the former case, and the period is 36 years and M 3 > 0.6M ⊙ in the latter case.  相似文献   

11.
We consider the evolutionary status of observed close binary systems containing black holes and Wolf-Rayet (WR) stars. When the component masses and the orbital period of a system are known, the reason for the formation of a WR star in an initial massive system of two main-sequence stars can be established. Such WR stars can form due to the action of the stellar wind from a massive OB star (MOB≥50M⊙), conservative mass transfer between components with close initial masses, or the loss of the common envelope in a system with a large (up to ～25) initial component mass ratio. The strong impact of observational selection effects on the creation of samples of close binaries with black holes and WR stars is demonstrated. We estimate theoretical mass-loss rates for WR stars, which are essential for our understanding the observed ratio of the numbers of carbon and nitrogen WR stars in the Galaxy \(\dot M_{WR} (M_ \odot yr^{ - 1} ) = 5 \times 10^{ - 7} (M_{WR} /M_ \odot )^{1.3} \). We also estimate the minimum initial masses of the components in close binaries producing black holes and WR stars to be ～25M⊙. The spatial velocities of systems with black holes indicate that, during the formation of a black hole from a WR star, the mass loss reaches at least several solar masses. The rate of formation of rapidly rotating Kerr black holes in close binaries in the Galaxy is ～3×10?6 yr?1. Their formation may be accompanied by a burst of gamma radiation, possibly providing clues to the nature of gamma-ray bursts. The initial distribution of the component mass ratios for close binaries is dN～dq=dM2/M1 in the interval 0.04?q0≤1, suggesting a single mechanism for their formation.  相似文献   

12.
Twenty-eight CS molecular clouds toward HII regions with Galactocentric distances from ～ 4 to 20 kpc have been studied based on observations obtained in the J=2→1 lines of CS and C34S on the 20-meter radio telescope of the Onsala Space Observatory (Sweden) in March 2001. All 28 clouds have been mapped with an angular resolution of ～40″. The peak intensity in the C34S line has been measured for 20 objects. An LTE analysis has been performed and the parameters of the molecular cloud cores derived. The core sizes are dA=0.3–4.8 pc, with a median value of ～1.6 pc. The mean hydrogen densities in the cloud cores are nH2=3.5×102–3.7 × 104 cm?3, with a median value of ～7.2×103 cm?3. The value of nH2 ends to decrease with increasing Galactocentric distance of the cloud. The masses of most clouds are 102?6×103M⊙, with the most probable value being MCS～103M⊙. The data follow the dependence MCS ∝d A (2.4–3.2) . As a rule, the cloud masses are lower than the virial masses for MCS<103M⊙.  相似文献   

13.
The possibility of applying the continuous wavelet analysis on the basis of a Poissonian core for the processing and interpretation of gravity and magnetic survey data is considered. Based on the wavelet spectrum, W(x,h), reconstruction of the initial signal, g(x), is possible. Additionally, based on this wavelet spectrum, the equivalent distributions of mass and magnetization that produce the initial field, g(x), can be reconstructed. These possibilities allow the wavelet transform to be used for solving such classical problems as the filtering of initial signals, continuation of the field, calculation of higher field derivatives in the upper and lower half-spaces, and reduction of magnetic anomalies to the pole.  相似文献   

14.
The equilibrium thickness of the isothermal layers of interstellar gas and volume gas densities ρ gas in the plane of the disk as a function of galactocentric distance R are computed for seven spiral galaxies (including the Milky Way) using an axisymmetrical model. In this model, the thickness of the stellar disk varies with R and remains approximately equal to the minimum thickness of a stable equilibrium disk. We found the disk thickness to increase toward the periphery in at least five of the seven galaxies. The density of the stellar disk decreases with R faster than ρ gas , so that gas dominates at the disk peripheries in terms of density. A comparison of the azimuthally averaged star formation rate SFR and the gas density shows the absence of a universal Schmidt law SFR ～ρ gas n for galaxies. However, the SFRs in various galaxies are better correlated with the volume than the gas surface density. The parameter n in the Schmidt law formally calculated using the least-squares method lies in the interval 0.8–2.4, being, on average, close to 1.5. The values of n calculated separately for the molecular gas display substantial scatter, but are, on average, close to unity. The value of n appears to increase with decreasing ρ gas , so that the fraction of gas that actively participates in star formation decreases with n.  相似文献   

15.
The synthesis of an analogue of the organic mineral evenkite included preparation of a mixture of ten individual molecular homologues of normal paraffin C n H2n + 2 (n = 19–28), melting of this mixture, and subsequent slow cooling under controlled conditions. The symmetrical distribution of these homologues by the number of carbon atoms in the molecule (dominant homologue n = 23) and the X-ray pattern of synthesized evenkite—a ten-component solid solution of n-paraffins—correspond to the characteristics of natural evenkite.  相似文献   

16.
We study the growth of the masses of neutron stars in binary systems due to the accumulation of mass from the optical donors accreted onto the neutron-star surface. Possible scenarios for this accretion are considered. The masses and magnetic-field strengths of radio pulsars derived using population-synthesis methods are compared to the observational data. The population-synthesis analysis indicates that a neutron star can increase its mass from the standard value of m x ? 1.35M⊙ to the Oppenheimer-Volkoff limit, m x ? 2.5M⊙, via accretion from a companion.  相似文献   

17.
Periodic variations of the position angle of the inner jet of the blazar S5 0716+71 suggest a helical structure for the jet. The geometrical parameters of a model helical jet are determined. It is shown that, when the trajectories of the jet components are non-ballistic, the angle between their velocity vectors and the line of sight lies in a broader interval than is the case for ballistic motions of the components, in agreement with available estimates. The contradictory results for the apparent speeds of components in the inner and outer jet at epochs 2004 and 2008–2010 can be explained in such a model. The ratio of the apparent speeds in the inner and outer jet are used to derive a lower limit for the physical speed of the components (β > 0.999) and to determine the pitch angle of the helical jet (p = 5.5°). The derived parameters can give rise to the conditions required to observe high speeds (right to 37c) for individual jet components.  相似文献   

18.
We have carried out numerical simulations of the dynamical evolution of galaxy clusters taking into account merging when the relative velocities of the colliding galaxies are low. In particular, we study the evolution of the structure, mass spectrum, and velocity spectrum of a cluster of a thousand galaxies, as well as the growth of the central supermassive cD galaxy. The initial velocity dispersion of the galaxies and the rotation of the cluster were taken into account. The observed logarithmic spectrum dN ～ \(\tfrac{{dM}}{M}\) was adopted as the initial mass spectrum. The dynamical evolution of galaxy clusters, allowing for the possible merging of colliding galaxies, results in the emergence of a central supermassive galaxy, whose mass continuously increases due to mergers. This occurs only if the mass of the central galaxy becomes greater than ～0.1 of the total mass of the cluster. The observation of cD galaxies with relative masses of ～0.01 suggests that they initially formed in the cluster core, merged with nearby galaxies, and accreted intergalactic gas. The model indicates that a logarithmic galaxy mass spectrum is preserved during the cluster evolution, despite the substantial decrease in the number of galaxies in the cluster with time. The model can also reproduce the observed mass distribution with distance from the cluster center, M r ～ r 1.7.  相似文献   

19.
Modern modeling of the population of low-mass X-ray binary systems containing black holes applying standard assumptions leads to a lack of agreement between the modeled and observed mass distributions for the optical components, with the observed masses being lower. This makes the task of estimating the systematic errors in the derived component masses due to imperfect models relevant. To estimate the influence of systematic errors in the derived masses of stars in X-ray binary systems, we considered two approximations for the tidally deformed star in a Roche model. Approximating the star as a sphere with a volume equal to that of the Roche lobe leads to slight overestimation of the equatorial rotational velocity V rot sin i, and hence to slight underestimation of the mass ratio q = M x /M v . Approximating the star as a flat, circular disk with constant local line profiles and a linear limb-darkening law (a classical rotational broadeningmodel) is an appreciably cruder approach, and leads to overestimation of V rot sin i by about 20%. In the case of high values of q = M x /M v , this approximation leads to substantial underestimation of the mass ratio q, which can reach several tens of percent. The mass of the optical star is overestimated by a factor of 1.5 in this case, while the mass of the black hole is changed only slightly. Since most estimates of component mass ratios for X-ray binary systems are carried out using a classical rotational broadening model for the lines, this leads to the need for appreciable corrections to (reductions of) previously published masses for the optical stars, which enhances the contradiction with the standard evolutionary scenario for low-mass X-ray binaries containing black holes.  相似文献   

20.
We have obtained the first estimates of the masses of the components of the Her X-1/HZ Her X-ray binary system taking into account non-LTE effects in the formation of the H γ absorption line: m x = 1.8 M ⊙ and m v = 2.5 M ⊙. These mass estimates were made in a Roche model based on the observed radial-velocity curve of the optical star, HZ Her. The masses for the X-ray pulsar and optical star obtained for an LTE model lie are m x = 0.85 ± 0.15 M ⊙ and m v = 1.87 ± 0.13 M ⊙. These mass estimates for the components of Her X-1/HZ Her derived from the radial-velocity curve should be considered tentative. Further mass estimates from high-precision observations of the orbital variability of the absorption profiles in a non-LTE model for the atmosphere of the optical component should be made.  相似文献   

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